A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is 6 StartRoot 2 EndRoot feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply. The triangle is isosceles. The leg-to-hypotenuse ratio is 1:StartRoot 2 EndRoot. The leg-to-hypotenuse ratio is 1:StartFraction StartRoot 2 EndRoot Over 2 EndRoot. The nonright angles are congruent. The ladder represents the longest length in the triangle.

The leg-to-hypotenuse ratio is 1/√2

The ladder represents the longest length in the triangle.

Step-by-step explanation:

The set up in the question will b a right angled triangle

Length of the ladder will be the hypotenuse

The distance from the base of the wall to the base of the ladder  is the adjacent

Height of the wall will be the opposite

Note that the longest side is always the hypotenuse (length of the ladder)

Given

length of the ladder = 12foot

The distance from the base of the wall to the base of the ladder = 6√2

The ratio of leg to hypotenuse = 6√2/12 = √2/2

√2/2 = √2/2 * √2/√2

√2/2 = √4/2√2

√2/2 = 2/2√2

√2/2 = 1/√2

Hence the leg-to-hypotenuse ratio is 1/√2

From the calculation the following are correct:

the leg-to-hypotenuse ratio is 1/√2

The ladder represents the longest length in the triangle.

2

step-by-step explanation:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl